Simplified Method to Account for Macro Dynamic Effects Influencing Global Friction Factors in Large Diameter Cross-Country Liquid Pipelines

Evidence associated with unaccounted macro dynamic effects influencing friction losses in large diameter cross-country liquid pipelines is examined with emphasis on back-calculated friction factors. Considerable amount of operating data is used to develop a simplified equation to estimate more realistic globally measured friction factor correspondent to the theoretical Darcy–Weisbach friction factor. This equation accounts for the summed effects of laminar sublayer, boundary roughness on the fluid profile plus, others cumulative and unaccounted macro dynamic effects normally occurring in curved pipes and in real-world cross-country liquid pipelines. The model has been developed and lately verified with reliable operating data from large crude and water cross country pipeline systems operating at large Reynolds numbers (104 < Re < 107) and covering a wide range of kinematic viscosity (1 cP < υ < 590 cP). Also, potential internal roughness growth, due to deposits and fouling, can be considered. The explicit equation was achieved by identifying a Karman–Prandtl type multiplier function and linked to the back-calculated global friction factors using the least squares technique with obtained coefficients of determination (R2) higher than 0.91, indicating the high reliability of the proposed method.